Descrizione del progetto
Approcci migliori per l’approssimazione del comportamento dei sistemi quantistici a molti corpi
Le proprietà fisiche dei sistemi quantistici a molti corpi sono generalmente descritte mediante le equazioni di Schrödinger. Tuttavia, è generalmente impossibile risolvere queste equazioni con le attuali tecniche numeriche. Pertanto, i fisici si avvalgono spesso di teorie dell’approssimazione nella pratica, che si concentrano solo su pochi comportamenti collettivi dei sistemi descritti. Attraverso le analisi matematiche, confermano se i modelli scelti descrivano con efficacia il comportamento dei sistemi. L’obiettivo complessivo del progetto RAMBAS, finanziato dall’UE, consiste nel giustificare alcune efficaci approssimazioni chiave impiegate nella fisica quantistica a molti corpi. Sfruttando nuove tecniche che derivano dall’analisi funzionale, dalla teoria spettrale, dal calcolo delle variazioni e dalle equazioni differenziali alle derivate parziali, RAMBAS si aspetta di portare le approssimazioni standard dei sistemi quantistici al livello successivo, fornendo ai fisici nuovi strumenti matematici.
Obiettivo
From first principles of quantum mechanics, physical properties of many-body quantum systems are usually encoded into Schroedinger equations. However, since the complexity of the Schroedinger equations grows so fast with the number of particles, it is generally impossible to solve them by current numerical techniques.
Therefore, in practice approximate theories are often applied, which focus only on some collective behaviors of the systems in question.
The corroboration of such effective models largely depends on mathematical methods. The overall goal of RAMBAS is to justify key effective approximations used in many-body quantum physics, including the mean-field, quasi-free, and random-phase approximations, as well as to derive subtle corrections in critical regimes.
Building on my unique expertise in mathematical physics, I will 1) develop general techniques to understand corrections to the mean-field and Bogoliubov approximations for dilute Bose gases, 2) introduce rigorous bosonization methods and combine them with existing techniques from the theory of Bose gases to understand Fermi gases, and 3) employ the bosonization structure of Fermi gases to study the many-body quantum dynamics in long time scales, thus deriving quantum kinetic equations.
By applying and suitably inventing mathematical techniques from functional analysis, spectral theory, calculus of variations and partial differential equations, RAMBAS will take standard approximations of quantum systems to the next level, with special focus on those particularly challenging situations where the particle correlation plays a central role but is yet not adequately addressed. RAMBAS will thereby provide the physics community with crucial mathematical tools, which are at the same time rigorous and applicable.
Campo scientifico
- natural sciencesphysical sciencesquantum physics
- natural sciencesmathematicsapplied mathematicsmathematical physics
- natural sciencesmathematicspure mathematicsmathematical analysisfunctional analysis
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equations
Parole chiave
Programma(i)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Argomento(i)
Meccanismo di finanziamento
HORIZON-ERC - HORIZON ERC GrantsIstituzione ospitante
80539 MUNCHEN
Germania